Page 236 - Principles and Applications of NanoMEMS Physics
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226 Appendix A
where the first term gives the electron kinetic energy,
ˆ
H = ¦¦ E c + c , (A.60)
0 k k σ k σ
σ =↑, ↓ k
and the second term gives the electron-electron Coulomb interaction,
ˆ
H = 1 ¦ V σ ′ σ c + c + c c . (A.61)
Int k k ′ σq ′ σ k + σq k − ′ q ′ σ ′ k ′ σ k σ
2 L
Solving for the eigenvalues and eigenfunctions of the problem is
facilitated by modeling the fermions in terms of bosons, in which case the
Hamiltonian becomes diagonal and it is easy to solve. The procedure that
accomplishes this fermion-to-boson transformation is called bosonization,
and is presented Appendix B.
